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Chapter 12: Problem 101

A solution concentration must be expressed in molality when considering boiling-point elevation or freezing-point depression but can be expressed in molarity when considering osmotic pressure. Why?

Short Answer

Expert verified
Molality is used for temperature effects; molarity for volume-based osmotic pressure.

Step by step solution

01

Define Molality and Molarity

Molality (\(m\)) is defined as the number of moles of solute per kilogram of solvent, i.e., \(m = \frac{n_{ ext{solute}}}{ ext{kg of solvent}}\). Molarity (\(M\)) is defined as the number of moles of solute per liter of solution, i.e., \(M = \frac{n_{ ext{solute}}}{ ext{L of solution}}\). Molality is independent of temperature, while molarity can change with temperature due to volume expansion or contraction of the solution.
02

Explain Why Molality is Used for Boiling and Freezing Points

Boiling-point elevation and freezing-point depression depend on colligative properties, which are properties that depend on the number of solute particles, not their identity. Because molality is mass-based and doesn't change with temperature, it is suitable for calculations involving changes in temperature, such as boiling and freezing points.
03

Explain Why Molarity is Used for Osmotic Pressure

Osmotic pressure involves the movement of molecules through a semi-permeable membrane and is volume-based. The volume of the solution is a crucial factor in osmotic pressure calculations, making molarity more suitable as it directly considers the volume of the solution. Since osmotic pressure is usually measured at a constant temperature, the variation in molarity with temperature has a minimal effect, making molarity an acceptable measure.
04

Summarize Key Points

In summary, molality is used for boiling-point elevation and freezing-point depression because it remains constant with temperature changes. Molarity, on the other hand, is used for osmotic pressure calculations because they inherently involve the volume of the solution, and these processes are typically at constant temperature.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Molality
Molality is a way of expressing concentration, essential when dealing with boiling-point elevation or freezing-point depression problems. It is denoted as 'm' and defined as the number of moles of solute per kilogram of solvent. This distinction is crucial: molality uses the mass of the solvent, not the whole solution, which includes the solute.
  • Temperature Independence: Since molality is based on mass, which doesn't change with temperature variations, it's a stable measure for experiments where temperature changes occur.
  • Mass-Based Measurement: By focusing on solvent mass, molality remains unaffected by thermal expansion or contraction, offering reliable results in varying thermal conditions.
Molality becomes particularly important when calculating colligative properties such as boiling-point elevation and freezing-point depression, highlighting its role in these processes.
Molarity
Molarity, denoted as 'M', is another common concentration measure. Unlike molality, molarity is defined as the number of moles of solute per liter of solution, considering the total solution volume, not just the solvent.
  • Volume-Based Measurement: Molarity considers the total volume of the solution, which makes it suitable for processes like osmotic pressure where the solution volume is a significant factor.
  • Temperature Dependency: Because molarity is volume-based, it can change with temperature as the solution expands or contracts. This dependency means it's generally used in conditions where the temperature remains constant.
While it's not ideal for problems involving temperature variation, the use of molarity is critical in cases like osmotic pressure measurement, which inherently involves solution volumes.
Boiling Point Elevation
Boiling point elevation is a colligative property observed when a solute is added to a solvent. The boiling point of a liquid increases when a solute is dissolved in it. This phenomenon occurs because solute particles disrupt the formation of bubbles necessary for boiling, requiring additional energy (or temperature) to reach the boiling point.
  • Colligative Nature: It depends on the number of solute particles, not their identity, meaning the effect is the same regardless of the type of solute, as long as the amount is constant.
  • Molality's Role: Because boiling point elevation relates to colligative properties, the concentration needs to be expressed in molality, not molarity, favoring a temperature-independent measure to account for the solute concentration accurately.
Understanding boiling point elevation is crucial for practical applications, such as antifreeze solutions or cooking at high altitudes.
Freezing Point Depression
Freezing point depression is another key colligative property, where the freezing point of a liquid decreases when a solute is added. Just like boiling point elevation, this property is influenced by the number of solute particles present.
  • Numerical Dependence: The decrease in freezing point is directly proportional to the number of solute particles in the solvent, emphasizing its colligative nature.
  • Reliance on Molality: Similar to boiling point elevation, freezing point depression requires the use of molality due to its measurement's temperature stability, ensuring consistent results.
Freezing point depression has multiple applications, including the use of salt to melt ice on roads in winter, showing its practical significance in real-world scenarios. Both colligative properties, boiling point elevation and freezing point depression, clearly illustrate why molality is favored in these cases.

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Most popular questions from this chapter

What is the value of the van't Hoff factor for \(\mathrm{KCl}\) if a \(1.00 \mathrm{~m}\) aqueous solution shows a vapor pressure depression of \(0.734 \mathrm{~mm} \mathrm{Hg}\) at \(298{ }^{\circ} \mathrm{C}\) ? (The vapor pressure of water at \(298 \mathrm{~K}\) is \(23.76 \mathrm{~mm} \mathrm{Hg} .\) )

Persons are medically considered to have lead poisoning if they have a concentration of greater than \(10 \mu \mathrm{g}\) of lead per deciliter of blood. What is this concentration in parts per billion? Assume that the density of blood is the same as that of water.

A \(0.944\) M solution of glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\), in water has a density of \(1.0624 \mathrm{~g} / \mathrm{mL}\) at \(20^{\circ} \mathrm{C}\). What is the concentration of this solution in the following units? (a) Mole fraction (b) Mass percent (c) Molality

What is the vapor pressure in \(\mathrm{mm} \mathrm{Hg}\) of the following solutions, each of which contains a nonvolatile solute? The vapor pressure of water at \(45.0^{\circ} \mathrm{C}\) is \(71.93 \mathrm{~mm} \mathrm{Hg}\). (a) A solution of \(10.0 \mathrm{~g}\) of urea, \(\mathrm{CH}_{4} \mathrm{~N}_{2} \mathrm{O}\), in \(150.0 \mathrm{~g}\) of water at \(45.0^{\circ} \mathrm{C}\) (b) A solution of \(10.0 \mathrm{~g}\) of LiCl in \(150.0 \mathrm{~g}\) of water at \(45.0^{\circ} \mathrm{C}\), assuming complete dissociation

Lactose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\), is a naturally occurring sugar found in mammalian milk. A \(0.335 \mathrm{M}\) solution of lactose in water has a density of \(1.0432 \mathrm{~g} / \mathrm{L}\) at \(20^{\circ} \mathrm{C}\). What is the concentration of this solution in the following units? (a) Mole fraction (b) Mass percent (c) Molality
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